Rivulet Flow Research Articles

An experimental study on the transient runback characteristics of wind-driven film/rivulet flows

A comprehensive experimental campaign was conducted to characterize the dynamic runback process of wind-driven water film/rivulet flows for a better understanding of the transient surface water transport process pertinent to aircraft icing phenomena. The experimental study was conducted by using an open-circuit wind tunnel to generate laminar boundary layer airflows with different freestream wind speeds to drive thin water film/rivulet flows over a flat test plate. A digital image projection (DIP) technique was used to achieve non-intrusive, temporally and spatially resolved measurements of the film thickness distributions to characterize the dynamic runback process of the wind-driven film/rivulet flow under different test conditions. Important characteristics of the wind-driven water runback process—such as the generation of well-organized two-dimensional (i.e., 2D) and more complicated three-dimensional (i.e., 3D) surface waves at air/water interfaces, stumbling runback motion of the film/rivulet heads in “acceleration-and-deceleration” cycles, breaking up the front contact lines to form multiple rivulet flows, meandering and merging of the rivulet flows—were revealed clearly and quantitatively based on the DIP measurements. A comprehensive force balance analysis was also performed to examine the variations of the relevant forces (i.e., the excess pressure forces built inside the film/rivulet flows, aerodynamic drag forces acting on the rivulet heads, and the restraining forces due to the surface tension along the liquid contact lines) and evaluate their importance in the breakoff of the stagnated film/rivulet heads to re-start the runback process of the wind-driven film/rivulet flows.

Gas-liquid flow in small channels: Artificial neural network classifiers for flow regime prediction

To design and operate multiphase apparatus with mini- and microchannels, it is important to know how the fluids stream inside. Most literature reports the occurrence of flow regimes in dependence on gas and liquid superficial velocities in flow maps that are valid for fluids with similar properties and channels with similar geometry. Attempts to develop universally applicable flow maps show limitations in the number and variation of considered model parameters or in the number of considered flow regimes. This paper presents artificial neural network classifiers able to predict all relevant flow regimes: (a) Taylor flow, (b) bubbly flow, (c) Taylor-annular flow, (d) churn flow, (e) dispersed flow, (f) annular flow, (g) rivulet flow, and h) parallel flow in dependence on geometric and operational parameters as well as fluid properties with a high precision (R=0.92...0.95 and classification rates were generally above 80%). The classifiers were developed and validated by using more than 13,000 experimental data on gas-liquid flows extracted from 97 flow maps and are based on 7 significant dimensionless groups, namely, ReG, ReL, WeG, WeL,CaL, Θ*, and the channel form factor FC.

Rivulet flow over and through a permeable membrane

Motivated by small-scale natural and industrial processes involving flow over and/or through a layer of a porous medium, a mathematical model for the steady gravity-driven flow of a slowly varying and thin rivulet of fluid over and through an even thinner permeable membrane is formulated and analyzed. The three-dimensional shape of the free surface of a rivulet with either fixed semi-width or fixed contact angle is determined, and it is shown how the length, base area and volume of the rivulet on the permeable part of the membrane depend on the physical properties of the system.

Two-Phase Flow Regimes and Heat Transfer Coefficients With R245fa in Manifolded-Microgap Channels

Manifold microchannels have shown high performance in embedded two-phase cooling of high heat flux electronics, demonstrating several examples of heat dissipation of 1 kW from 1-cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> chips, with low pumping power requirements. The heat transfer coefficients (HTCs) in previous studies of chip-scale manifold-microchannel coolers exhibited a peak at relatively low quality (about 0.2–0.4) and steeply declined thereafter with increasing quality. However, manifold microchannels—arrays of manifolded-microgap channels—are a more complex geometry than traditional, straight, and circular channels and therefore generate more complex two-phase flow phenomena, which influences the resulting heat transfer performance. To better characterize the flow and heat transfer in such channels, in this study, the fluid flow and wall heat transfer in a visualization test section was imaged with a high-speed optical camera and thermography. R245fa served as the working fluid due to its low-pressure operation (approximately 1.8 atm at 30 °C) and excellent thermal properties, including high latent heat, high specific heat, and high thermal conductivity. The results are reported in terms of the channel outlet flow regime and HTCs under varying heat fluxes and mass fluxes with two manifold designs. The flow regimes and HTCs are compared with well-regarded predictive relations developed for more traditional channel geometries. The emergence of intermittent, and then persistent, dryout was associated with intermittent rivulet flow at the channel outlet and was observed to cause declining average wall HTCs, even while high HTCs occurred at the consistently wetted inlet region.

Waves in a rivulet falling down an inclined cylinder

AbstractIn the long‐wave approximation, a theoretical model is developed to describe waves in a rivulet flowing down the lower surface of an inclined cylinder. The model equations are derived by the weighted residual method by projecting the Navier–Stokes equations onto the constructed system of basic orthogonal polynomials. The simplest case of quasi‐two‐dimensional waves is studied in detail. The stability of the rivulet flow is analyzed and dispersion dependences for linear waves are obtained. The characteristics of nonlinear steady‐state traveling waves have been obtained by numerical method for the first time, and the spatial development of forced waves has been studied. The results of calculations are in good agreement with the available experimental data for various liquids in a wide range of parameters.

Uncertainty of rivulet flows on heterogeneous surfaces – A numerical study

This paper presents a three-dimensional numerical simulation of water flow on an inclined plate using the software package OpenFOAM. We specifically investigate the influence of a heterogeneous surface on the flow pattern and the degree of wetting. By analyzing 400 simulation results a recently developed method for applying random contact angle inhomogeneities to surfaces is investigated. The simulations were carried out using the empirical contact angle model, which enables stable rivulet development. Part of the analysis is conducted with the help of the statistical software Dakota, which provides information about the probability distribution of the amount of wetted area when varying the two important influencing factors: the amplitude of the contact angle disturbance or the size of contiguous hydrophobic or hydrophilic areas. The results show that a variation of the two input parameters as desired leads to the introduction of a random component and thus to a change in the flow behavior. However, the changes remain within a narrow range around the mean value and produce only a few outliers, which occur mainly at large contact angle disturbance amplitudes and thus indicate the determining influence of the amplitude. The method has proven useful for performing several runs of the same simulation configuration for collecting statistics. Furthermore the inclination of the plate and the contact angle using a constant contact angle model are varied. Here, a clear dominance of the influence of the inclination also manifests over a wide contact angle range.

Rivulet flow down a slippery substrate

A detailed analysis of small-scale locally unidirectional gravity-driven rivulet flow with prescribed volume flux down an inclined slippery substrate for a rivulet with either constant width (i.e., pinned contact lines) or constant contact angle is undertaken. In particular, we determine the effect of varying the Navier slip length λ (i.e., the strength of the slip at the solid–fluid interface) on the rivulet. The present analysis shows that the shape and size of the rivulet and the velocity within it depend strongly on the value of λ. Increasing the value of λ reduces the viscous resistance at the substrate and, hence, leads to a larger velocity within the rivulet, and so the prescribed flux is achieved with a smaller rivulet. In particular, in the limit of strong slip, λ → ∞, for a rivulet of a perfectly wetting fluid and a rivulet with constant width, the velocity becomes large and plug-like like O(λ1/2) ≫ 1, and the rivulet becomes shallow like O(λ−1/2) ≪ 1, while for a rivulet with positive constant contact angle, the velocity becomes large and plug-like like O(λ2/3) ≫ 1, and the rivulet becomes narrow like O(λ−1/3) ≪ 1 and shallow like O(λ−1/3) ≪ 1.

An experimental study to characterize the effects of initial ice roughness on the wind-driven water runback over an airfoil surface

In the present study, an experimental study was conducted to characterize the effects of initial ice roughness on the transient behaviors of surface water/ice run-back over a NACA 23012 airfoil model under a glaze icing condition. The experimental study was conducted in the Icing Research Tunnel of Iowa State University (i.e., ISU-IRT). A digital image projection (DIP) technique was applied to provide non-intrusive, temporally-and-spatially-resolved measurements of the thickness distributions of the dynamic water/ice flows over the airfoil surface. Two typical surface morphologies were observed for the surface water runback over the airfoil models: water film flow and water rivulets flow. While the surface water film flow modulated with one primary wave and multiple secondary waves is observed at lower wind speed conditions (i.e., U∞ = 10 m/s), the water rivulets flow is observed at relatively higher wind speed conditions (i.e., U∞ = 15 m/s). The initial ice roughness is found to retard and shorten the primary wave formation in the water film flow. It is also found that the initial ice roughness could trap and decelerate the water flow and decrease the inertia force in the film front, which essentially delays the formation of the rivulets. The water rivulet flow trapped by the initial roughness was found to have a meandering behavior, due to which, the initially formed narrow rivulets merged into wider rivulets as they move downstream. By recognizing the film/rivulets boundary during the dynamic surface water/ice runback process, the quantitative details were extracted, i.e., the formation, transition, and development of the rivulet flows. The initial ice roughness was found to have a significant effect on the rivulet characteristics (e.g., rivulet width, spacing, and height).

Effectiveness factors for a partially wetted catalyst based on the rivulet flow model

Partial wetting is a common phenomenon in a trickle bed reactor, which causes nonuniform mass transfer flux at the external surface of the catalyst. Previous work on effectiveness factor for a partially wetted catalyst are mainly based on the assumption that the spherical catalyst is wetted by a liquid film. In fact, it is only true when the liquid-solid contact angle is very small. In most situations, rivulet flow prevails. The purpose of the article is to calculate effectiveness factors for both gas-limited and liquid-limited reactions under the two wetting modes by using finite element method (FEM). The effects of wetting efficiency, Biot number, and Thiele modulus on effectiveness factors are investigated. On the basis of the FEM results, the intrinsic reason for the variation of effectiveness factors with respect to wetting efficiency is revealed, and good agreements are observed between this work and the conventional models.

An experimental investigation on the dynamic glaze ice accretion process over a wind turbine airfoil surface

Icing events, particularly under precipitation-icing conditions in which high-liquidity glaze ice tends to form, could pose significant threats to the safe and effective operations of wind turbines in cold and wet environments. During the glaze ice accretion process, the wind-driven unfrozen water was coupled with the growth of ice structures and difficult to be quantified and characterized. In the present study, we introduced a Digital Image Projection (DIP) technique to quantitatively measure the unsteady water runback behaviors and dynamic ice accretion process under typical glaze icing conditions over a highly-cambered wind turbine airfoil surface, i.e., the pressure-side surface of DU91-W2-250 airfoil, in the Icing Research Tunnel at Iowa State University (ISU-IRT). DIP measurement results were found to be able to successfully capture the time-resolved three-dimensional information of the water transport behaviors over the ice accreting surface of the airfoil model during the glaze icing processes. The stumbling motions of the rivulet flows were observed during the icing processes, coupled with an increasing fluctuations induced by the underneath ice roughness. The forces acting on the rivulet flows were analyzed, and a theoretical model based on the force balance was built to predict the rivulet flows. The effects of the incoming airflow velocity on the glaze icing process over the airfoil surface were also studied, and it was found that, as the incoming flow velocity increased, the runback rivulet flows would move farther downstream and became thinner and narrower due to the increased aerodynamic stress acting on them. The rivulet bulged shape was found to have an inverse relationship with the inflow velocity squared. In addition, the ice accreted over the airfoil surface during an icing process was quantitatively decoupled from the unfrozen wind-driven water, and the quantitative results can be used to validate and optimize current ice accretion models.

Simulating thin film flow using the shallow water equations and smoothed particle hydrodynamics

The shallow water equations are discretized using the smoothed particle hydrodynamics (SPH) method. This combination is applied to the simulation of a small scale thin fluid film on partially wetted and curved surfaces. The simulation incorporates all relevant forces, including surface tension and the contact angle force at the separating line between dry and wet regions. The resulting rivulet flow is validated using theoretical findings and measurements carried out elsewhere.

Destruction of waves and formation of rivulets on the surface of a heated liquid film at Re = 10

The mechanism of transformation of developed naturally formed waves into thermocapillary-wave structures in the vertical flow of a heated water film was studied experimentally. The motion of large waves whose width significantly exceeds the distance between the thermocapillary rivulets (transverse inhomogeneities of thickness and temperature), which have already formed in the residual film layer in front of the incoming large wave was studied in detail. It is shown that combination of thermocapillary and inertial effects in a wavy liquid film leads to deformation of large waves and their decay into the waves of a smaller width. Various scenarios of large wave destruction are considered. It is found out that when medium and small waves move, the thermocapillary forces change the distance between their crests, adjusting them to the distance between the forming structures in the residual layer.The regime maps, where the flow is divided into two zones: the region of deformation of three-dimensional waves and the region of developed rivulet flow, have been plotted for different heat fluxes.Various scenarios of changes in three-dimensional waves occur in the region of their deformation. In the region of developed rivulet flow, the motion of waves obeys the general laws. Waves propagate only along the rivulets with the average inter-rivulet distance equal to five capillary constants. Between the rivulets, the film is smooth. The amplitude of waves (the maximal film thickness) in the rivulets and their velocity increase as they move along the heater.

An Experimentally Derived Model to Predict the Water Film in a Compressor Cascade With Droplet Laden Flow

In recent years, overspray fogging has become a powerful means for power augmentation of industrial gas turbines. Despite the positive thermodynamic effect on the cycle, droplets entering the compressor increase the risk of water droplet erosion and deposition of water on the blades leading to an increase of required torque and profile loss. Due to this, detailed information about the structure and the amount of water on the surface is key for compressor performance. Experiments were conducted with a droplet laden flow in a transonic compressor cascade focusing on the film formed by the deposited water. Two approaches were taken. In the first approach, the film thickness on the blade was directly measured using white light interferometry. Due to significant distortion of the flow caused by the measurement system, a transfer of the measured film thickness to the undisturbed case is not possible. Therefore, a film model is adapted to describe the film flow in terms of height averaged film parameters. In the second approach, experiments were conducted in an undisturbed cascade setup and the water film pattern was measured using a nonintrusive quantitative image processing tool. Utilizing the measured flow pattern in combination with findings from the literature, the rivulet flow structure is resolved. From continuity of the water flow, a film thickness is derived showing good agreement with the previously calculated results. Using both approaches, a three-dimensional (3D) reconstruction of the water film pattern is created giving first experimental results of the film forming on stationary compressor blades under overspray fogging conditions.

Flow Regimes of Viscous Immiscible Liquids in T‐Type Microchannels

AbstractA computational and experimental study of the flow regimes of a mixture of castor and paraffin oils in a T‐type microchannel with 200 × 400 µm cross section was carried out. The ranges of parallel, slug, droplet, and rivulet flow regimes of the tested mixture were defined. According to the experimental results, a flow regime map was constructed for this mixture depending on the Weber number multiplied by the Ohnesorge number. A correlation of the length of paraffin oil slugs to the fluid flow ratio was established. The experimental data were compared with results of numerical simulation. A good agreement between calculation and experimental data was achieved in terms of reproduction of flow regimes, phase boundaries, and slug length.

Analogue Fracture Experiments and Analytical Modeling of Unsaturated Percolation Dynamics in Fracture Cascades

Core IdeasMass redistribution at unsaturated fracture intersections depends on free‐surface flow modes.A Washburn‐type flow regime is recovered via an analytical solution for capillary fracture inflow.A Gaussian transfer function predicts mass partitioning for arbitrary‐sized fracture cascades.Infiltration and recharge dynamics in fractured aquifer systems often strongly deviate from diffuse Darcy–Buckingham type flows due to the existence of a complex gravity‐driven flow component along fractures, fracture networks, and fault zones. The formation of preferential flow paths in the unsaturated or vadose zone can trigger rapid mass fluxes, which are difficult to recover by volume‐effective modeling approaches (e.g., the Richards equation) due to the nonlinear nature of free‐surface flows and mass partitioning processes at unsaturated fracture intersections. In this study, well‐controlled laboratory experiments enabled the isolation of single aspects of the mass redistribution process that ultimately affect travel time distributions across scales. We used custom‐made acrylic cubes (20 by 20 by 20 cm) in analog percolation experiments to create simple wide‐aperture fracture networks intersected by one or multiple horizontal fractures. A high‐precision multichannel dispenser produced gravity‐driven free‐surface flow (droplets or rivulets) at flow rates ranging from 1 to 5 mL min−1. Total inflow rates were kept constant while the fluid was injected via 15 (droplet flow) or three inlets (rivulet flow) to reduce the impact of erratic flow dynamics. Normalized fracture inflow rates were calculated and compared for aperture widths of 1 and 2.5 mm. A higher efficiency in filling an unsaturated fracture by rivulet flow observed in former studies was confirmed. The onset of a capillary‐driven Washburn‐type flow was determined and recovered by an analytical solution. To upscale the dynamics and enable the prediction of mass partitioning for arbitrary‐sized fracture cascades, a Gaussian transfer function was derived that reproduces the repetitive filling of fractures, where rivulet flow is the prevailing regime. Results show good agreement with experimental data for all tested aperture widths.

Physical modelling of the motion of a liquid metal melt along the surface of a heated rod

The investigation of the melt flow of a liquid metal along the surface of a heated rod is carried up. In the experiments, the metal from the upper volume was drained over the surface of a quartz tube, heated from the inside. This pipe is used to simulate a fuel column. A high-speed video of the process was produced. Data are obtained on the features of the flow of a metal melt. The stages of formation of droplets are shown. The data on the shape and velocity of the droplet movement are given. It is shown that in the air atmosphere around the test section when the first drop passes on the surface of quartz, a trace is formed, along which the metal moves in the future. Direct and curvilinear rivulet flows on the rod's surface are also observed.

Experimental investigation of heat transfer in a rivulet driven by gas flow in a minichannel

The heat transfer in a shear driven rivulet flow at isothermal conditions in a minichannel has been studied. The experiments were conducted using the setup, specially designed for the shear driven rivulet flow. The effect of liquid flow rate and substrate temperature on the width of the rivulet was studied experimentally using Laser induced fluorescence technique (LIF). The temperature distribution for different time moments of the rivulet surface was measured by the FLIR infrared (IR) camera. IR-measurements served to demonstrate that rivulet surface temperature is lower than substrate one due to liquid evaporation from the rivulet surface.

Experimental investigation of the influence of flow rate pulsations on the rivulet flow regime

The influence of flow rate pulsations on the rivulet flow regime has been investigated. The experiments were carried out on the underside of a smooth polyethylene plate. The investigation has shown that the influence of flow rate pulsations on the stream patterns is determined by flow peculiarities in the steady-state regime. Disturbances arising from pulsations of liquid flow rate can affect the stream liquid pattern of the rivulet. Such disturbance can cause the development of latent instability at individual points situated along the length of rivulet. The greatest effect on the stream structure is observed for the flow rate pulsation at liquid discharge with the ambiguity of rivulet regime. If the flow rate pulsations affect periodically the meandering rivulet, then it is possible to reduce the degree of meandering and convert the stream into the straight rivulet. In the regime of unstable meandering, it is impossible to identify correctly the effects caused by the flow rate pulsations at the initial area of the rivulet because of great self-acting pulsations of flow rate appearing in different sections along the rivulet.

Two-phase frictional pressure drop in a thin mixed-wettability microchannel

This study focuses on the experimental investigation of the two-phase pressure drop in a thin mixed-wettability microchannel. Air-water flows in a thin microchannel of dimensions 3.23 mm wide by 0.304 mm high. The test conditions primarily produce rivulet flow. The two-phase pressure drop increases when the base contact angle changes from 76° to 99°, with the other walls remaining the same. Combining the result with existing literature demonstrates that consistent behavior in the change of the two-phase pressure when comparing different wettabilities arises with careful consideration of the experimental parameters to classify experiments of adiabatic two-phase flow in a single microchannel into three categories: homogeneous, hydrophobic mixed-wettability, and superhydrophobic mixed-wettability microchannels. The two-phase pressure measurements also allow for the assessment of homogeneous, separated, and relative permeability models. Limiting the analysis to the rivulet flow regime allows for the determination of a new relative permeability exponent of 1.747 in the two-fluid model, which produces a mean absolute percent error of 14.9%. However, the models do not fully collapse the data, indicating differing air-water interactions. The work discusses possible causes of this behavior from experimental limitations to instabilities of the rivulet flow.

Rivulet flow of generalized Newtonian fluids

Steady unidirectional gravity-driven flow of a uniform thin rivulet (i.e. a rivulet with small transverse aspect ratio) of a generalised Newtonian fluid down a vertical planar substrate is considered. The parametric solution for any generalised Newtonian fluid whose viscosity can be expressed as a function of the shear rate, and the explicit solution for any generalised Newtonian fluid whose viscosity can be expressed as a function of the extra stress are obtained. These general solutions are used to describe rivulet flow of Carreau and Ellis fluids, highlighting the similarities and differences between the behaviour of these two fluids. In addition, the general behaviour of rivulets of nearly Newtonian fluids and of rivulets with small or large prescribed flux, as well as the behaviour of rivulets of strongly shear-thinning Carreau and Ellis fluids, are also described. It is found that whereas the monotonic dependence of the viscosity of a Carreau fluid on its three non-dimensional parameters and of an Ellis fluid on two of its three non-dimensional parameters leads to the expected dependence of the behaviour of the rivulet on these parameters (namely that increasing the viscosity of the fluid leads to a larger rivulet), the non-monotonic dependence of the viscosity of an Ellis fluid on the non dimensional parameter that measures the degree of shear thinning leads to a more complicated dependence of the behaviour of the rivulet on this parameter. In particular, it is also found that when the maximum extra stress in the rivulet is sufficiently large a rivulet of an Ellis fluid in the strongly shear-thinning limit in which this parameter becomes large comprises two regions with different viscosities. In the general case of non-zero viscosity in the limit of large extra stress the two regions have different constant viscosities, whereas in the special case of zero viscosity in the limit of large extra stress one region has constant viscosity and the other has a non-constant power-law viscosity, leading to a plug-like velocity profile with large magnitude in the narrow central region of the rivulet.